Problem: Simplify the following expression: $k = \dfrac{t^2 - 4t - 45}{t + 5} $
Solution: First factor the polynomial in the numerator. $ t^2 - 4t - 45 = (t + 5)(t - 9) $ So we can rewrite the expression as: $k = \dfrac{(t + 5)(t - 9)}{t + 5} $ We can divide the numerator and denominator by $(t + 5)$ on condition that $t \neq -5$ Therefore $k = t - 9; t \neq -5$